Can't Penetrate Your Girlfriend

It sounds like your girlfriend is suffering from vaginisimus, which is an involuntary contraction of the lower third of the vagina.  This problem is usually caused by emotional conflicts. For example, if a woman is afraid to become involved, her body may involuntarily close its doors, thereby preventing contact.  Oftentimes vaginisimus is associated with previous sexual abuse.   

The only way for your girlfriend to resolve the problem is to see a good sex therapist or psychotherapist.  Treatment will consist of talking therapy along with exercises that she can do on her own to learn to relax the muscles.  However, exercises alone, without insight, will be of little help.  So, tell your girlfriend what I said and, if she is afraid to go alone, go with her to talk to a sex therapist. 

One of the things you will want to determine is when the problem began.  You said that she has been without a partner for five years.  Did she have the problem with her previous partner?  If not, then she will need to examine why the problem has developed since her break up?  Is she afraid to get close and break up again?  All of this will need to be discussed and resolved in therapy.  

Don't be downhearted.  The problem can be solved.